@HdudePhoenix Do you have any other drives on your computer? If you do, you may want to check your program files folders on those (if you have 64 bit Windows, be sure to check both Program Files and Program Files (x86)).
If you installed from disk, it's possible the game may have installed to a Bioware folder (it's been quite a few years since I installed the ME games from disk, so I can't quite remember), so it might be worth looking for a Bioware folder in your program files, or even an EA folder. Did you install from disk every time you reinstalled? After installing from disk, did the game update to the final version?
Have you tried doing a repair of the game in Origin? Might do nothing, but it's worth a try. Just right click the game in Origin and select 'repair game'.
For future reference, you can check where Origin is set to install games by going to the menu in Origin, going to application settings and choosing advanced. Since pictures tend to do a better job of explaining than I'm capable of at the moment, here's a screenshot:
The "Your games will be installed to the following location:" part is what you're looking for.
I do have another drive, but I don't even see a program folder on that one, so I believe they aren't there. Thanks for explaining how to find where games are installed, you were right it was installed to an EA folder. I only installed from disk the first time installed it, I've downloaded from online since. The game is up to date to the most recent version I believe, all the DLC is installed. I ran a repair on it, but sadly no joy ☹️
